The Meldrum Co. is analyzing a proposed project. The company expects to sell 3,000 units,give or take 15%. The expected variable cost per unit is $8 and the expected fixed costs are $12,500. Cost estimates are considered accurate within a plus or minus 5% range. The depreciation expense is $4,000. The sale price is estimated at $18 a unit,give or take 2%. The company bases its sensitivity analysis on the expected case scenario. What is the amount of the fixed cost per unit under the pessimistic case scenario?
A) $4.17
B) $4.66
C) $5.15
D) $5.35
E) $6.02

Question

Quizplus · Accepted Answer

First, let's calculate the expected case scenario:

Expected units sold = 3,000
Variable cost per unit = $8
Expected fixed costs = $12,500
Depreciation = $4,000

Revenue per unit = $18

Expected Revenue = 3,000 units x $18 per unit = $54,000
Expected Variable Costs = 3,000 units x $8 per unit = $24,000
Contribution Margin = $54,000 - $24,000 = $30,000
Expected Income before Depreciation and Taxes = $30,000 - $12,500 - $4,000 = $13,500

Now let's calculate the pessimistic case scenario:

Units sold (15% below expected) = 2,550 units
Units sold (15% above expected) = 3,450 units

Variable cost per unit = $8

Fixed costs (5% below expected) = $11,875
Fixed costs (5% above expected) = $13,125

Depreciation = $4,000

Revenue per unit (2% below expected) = $17.64
Revenue per unit (2% above expected) = $18.36

Pessimistic case scenario revenue:

2,550 units x $17.64 per unit = $44,961
3,450 units x $18.36 per unit = $63,342

Pessimistic case scenario total cost:

Fixed costs (5% below expected) = $11,875
Fixed costs (5% above expected) = $13,125

Variable costs:

2,550 units x $8 per unit = $20,400
3,450 units x $8 per unit = $27,600

Depreciation = $4,000

Pessimistic case scenario Income before Depreciation and Taxes:

Case (fixed costs = $11,875) and (sales = $44,961):
$44,961 - $20,400 - $11,875 - $4,000 = $8,686

Case (fixed costs = $13,125) and (sales = $63,342):
$63,342 - $27,600 - $13,125 - $4,000 = $ 18,617

Now we can calculate the fixed cost per unit in the pessimistic case scenario as follows:

For the case with low sales and low fixed costs:

Fixed costs (5% below expected) = $11,875

Units sold (15% below expected) = 2,550

Fixed cost per unit = $11,875 / 2,550 = $4.66

Therefore, the answer is (C) $5.15.